In the Sun, deuterium-producing events are so rare (diprotons, the much more common result of nuclear reactions within the star, immediately decay back into two protons) that a complete conversion of the star's hydrogen would take more than 1010 (ten billion) years at the prevailing conditions of its core.[2] The fact that the Sun is still shining is due to the slow nature of this reaction; if it went more quickly, the Sun would have exhausted its hydrogen long ago.

The theory that proton–proton reactions are the basic principle by which the Sun and other stars burn was advocated by Arthur Stanley Eddington in the 1920s. At the time, the temperature of the Sun was considered too low to overcome the Coulomb barrier. After the development of quantum mechanics, it was discovered that tunneling of the wavefunctions of the protons through the repulsive barrier allows for fusion at a lower temperature than the classical prediction.

This first step is extremely slow because the beta-plus decay of the diproton to deuterium is extremely rare (the vast majority of the time, the diproton decays back into hydrogen-1 through proton emission). The half-life for a successful p-p fusion in the core of the Sun is estimated to be a billion years, even at extreme density and temperatures found there.

The positron emitted by the beta-decay is almost immediately annihilated with an electron, and their mass energy, as well as their kinetic energy, is carried off by two gamma rayphotons.

This process, mediated by the strong nuclear force rather than the weak force, is extremely fast by comparison to the first step. It is estimated that, under the conditions in the Sun's core, a newly-created deuterium nucleus exists for only about 4 seconds before it is converted to He-3.

From here there are four possible paths to generate 4He. In pp I, helium-4 is produced by fusing two helium-3 nuclei; the pp II and pp III branches fuse 3He with pre-existing 4He to form beryllium-7, which undergoes further reactions to produce two helium-4 nuclei. In the Sun, the helium-3 produced in these reactions exists for only about 400 years before it is converted into helium-4.[4]

In the Sun, 4He synthesis via branch pp I occurs with a frequency of 86%, pp II with 14% and pp III with 0.11%. There is also an extremely rare pp IV branch. Additionally, other even less frequent reactions may occur; however, the rate of these reactions is very low due to very small cross-sections, or because the number of reacting particles is so low that any reactions that might happen are statistically insignificant. This is partly why no mass-5 or mass-8 elements are seen. While the reactions that would produce them, such as a proton + helium-4 producing lithium-5, or two helium-4 nuclei coming together to form beryllium-8, may actually happen, these elements are not detected because there are no stable isotopes of mass 5 or 8; the resulting products immediately decay into their initial reactants.

The complete pp I chain reaction releases a net energy of 26.22 MeV. Two percent of this energy is lost to the neutrinos that are produced.[5] The pp I branch is dominant at temperatures of 10 to 14 MK. Below 10 MK, the PP chain does not produce much 4He.[citation needed]

Note that the energies in the equation above are not the energy released by the reaction. Rather, they are the energies of the neutrinos that are produced by the reaction. 90% of the neutrinos produced in the reaction of 7Be to 7Li carry an energy of 0.861 MeV, while the remaining 10% carry 0.383 MeV. The difference is whether the lithium-7 produced is in the ground state or an excited state, respectively.

This reaction is predicted but has never been observed due to its rarity (about 0.3 ppm in the Sun). In this reaction, Helium-3 reacts directly with a proton to give helium-4, with an even higher possible neutrino energy (up to 18.8 MeV).

Comparing the mass of the final helium-4 atom with the masses of the four protons reveals that 0.007 or 0.7% of the mass of the original protons has been lost. This mass has been converted into energy, in the form of gamma rays and neutrinos released during each of the individual reactions. The total energy yield of one whole chain is 26.73 MeV.

Energy released as gamma rays will interact with electrons and protons and heat the interior of the Sun. Also kinetic energy of fusion products (e.g. of the two protons and the 4
2He from pp-I reaction) increases the temperature of plasma in the Sun. This heating supports the Sun and prevents it from collapsing under its own weight.

Neutrinos do not interact significantly with matter and therefore do not help support the Sun against gravitational collapse. Their energy is lost: the neutrinos in the ppI, ppII and ppIII chains carry away 2.0%, 4.0%, and 28.3% of the energy in those reactions, respectively.[6]

In the Sun, the frequency ratio of the pep reaction versus the pp reaction is 1:400. However, the neutrinos released by the pep reaction are far more energetic: while neutrinos produced in the first step of the pp reaction range in energy up to 0.42 MeV, the pep reaction produces sharp-energy-line neutrinos of 1.44 MeV. Detection of solar neutrinos from this reaction were reported by the Borexino collaboration in 2012.[7]

Both the pep and pp reactions can be seen as two different Feynman representations of the same basic interaction, where the electron passes to the right side of the reaction as an anti-electron. This is represented in the figure of proton–proton and electron-capture chain reactions in a star, available at the NDM'06 web site.[8]